How to rig for game engines?
In the BGE you can use your rig as it is but you have to animate using the Action Editor. To play these animations you need to use the action actuator. 

If you want to use the rig in Unity you simply just need to export the rig from Blender as *.fbx. Select 'Armatures' in the export options. When importing to Unity you have to select 'Rig' in the import settings.

I don't know much about CryEngine but you might consider taking a look at the addon 'CryBlend'.

As far as I know you can import *.fbx files in Stingray too, so it's the same steps I explained above for Unity.